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Quads (Naked and Hidden) Technique
1Definition: Quads are similar to Triples, except that four candidates are spread out over four cells of the same Lane or Block, instead of just three candidates in three cells.
Naked Quads are Quads where no other candidates appear in the four cells.
Hidden Quads are Quads in which other candidates appear in one or more of the cells, but the four candidates of the Quad do not appear elsewhere in the Lane or Block shared by the four cells.
Naked Quads are Quads where no other candidates appear in the four cells.
Hidden Quads are Quads in which other candidates appear in one or more of the cells, but the four candidates of the Quad do not appear elsewhere in the Lane or Block shared by the four cells.
2Look For: Four cells with only the same four candidates, or subset of the four candidates (Naked Quads.)
Or four candidates that only appear in four cells in the same Lane or Block, where other candidates appear in one of more of the four cells (Hidden Quads.)
Or four candidates that only appear in four cells in the same Lane or Block, where other candidates appear in one of more of the four cells (Hidden Quads.)
3Consequence: For Naked Quads: The four candidates can be erased from all other cells in the shared Lane or Block (or, if the Quads share the same Lane and Block, then erase from the shared Block as well as from the shared Lane.)
For Hidden Quads Erase every other candidate from the Quads' cells (in effect turning the Hidden Quad into a Naked Quad, which may allow for further erasures if the cells of the Quad all share the same Lane and Block.)
For Hidden Quads Erase every other candidate from the Quads' cells (in effect turning the Hidden Quad into a Naked Quad, which may allow for further erasures if the cells of the Quad all share the same Lane and Block.)
4Why it Works: For a Quad, there are four candidate numbers spread over four cells. So we know that each of the four cells will contain one of the four candidates. This leaves nowhere else in the shared Lane/Block for these four candidates to go. So, if these candidates appear in other cells of the shared Lane/Block, they can be erased, and if other candidates appear in the Quad's cells they can be erased.
5In our example, there are four cells that contain only the candidates 1, 5, 7, and 9. That makes those cells a Naked Quad.
Just as with Naked Pairs and Naked Triples, any of those candidates appearing outside of the Quad cells in the shared Lane [or Block, if all of the Quad cells are in the same Block] can be erased.
(This makes the 5 on I8 a Hidden Single, and so solves that cell.)
Just as with Naked Pairs and Naked Triples, any of those candidates appearing outside of the Quad cells in the shared Lane [or Block, if all of the Quad cells are in the same Block] can be erased.
(This makes the 5 on I8 a Hidden Single, and so solves that cell.)
6Your Turn!
This has created a new Naked Quad in Block 3. In order to continue with this tutorial, identify the Quad, and then erase the Quad's candidates from all non-Quad cells in the Block.
This has created a new Naked Quad in Block 3. In order to continue with this tutorial, identify the Quad, and then erase the Quad's candidates from all non-Quad cells in the Block.
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